Kerr Newman

Black Holes · Part 2

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Table of Contents

  1. 1.The General Black Hole Solution
  2. 2.Kerr-Newman Metric in Boyer-Lindquist Coordinates
  3. 3.Horizons and Ring Singularity
  4. 4.Ergosphere
  5. 5.Black Hole Thermodynamics
  6. 6.Astrophysical Relevance
  7. 7.Summary
  8. 8.Navigation
  9. 9.⚡ No-Hair Theorem
  10. 10.📐 Geometric Properties

Key Equations

$$\begin{align} ds^2 &= -\frac{\Delta - a^2\sin^2\theta}{\Sigma}c^2dt^2 - \frac{2ar_s\sin^2\theta}{\Sigma}(c\,dt)(d\phi) \\ &\quad + \frac{\Sigma}{\Delta}dr^2 + \Sigma d\theta^2 \\ &\quad + \frac{(r^2+a^2)^2 - a^2\Delta\sin^2\theta}{\Sigma}\sin^2\theta\, d\phi^2 \end{align}$$
$$r_\pm = \frac{r_s}{2} \pm \sqrt{\left(\frac{r_s}{2}\right)^2 - a^2 - r_Q^2} = \frac{GM}{c^2} \pm \sqrt{\frac{G^2M^2}{c^4} - a^2 - \frac{GQ^2}{c^4}}$$
$$\kappa = \frac{c^2(r_+ - r_-)}{2(r_+^2 + a^2)}$$
$$S_{BH} = \frac{k_BA_+}{4\ell_P^2} = \frac{\pi k_Bc(r_+^2 + a^2)}{\hbar G}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Black Holes course on CoursesHub.World. Study the physics of black holes from Schwarzschild geometry to Hawking radiation. Covers rotating and charged black holes, thermodynamics, the information paradox, holographic principle, and astrophy...

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